Past records suggest that the mean annual income,

1

, of teachers in state of Texas is greater than or equal to the mean annual income,

2

, of teachers in Virginia. In a current study, a random sample of10

teachers from Texas and an independent random sample of10

teachers from Virginia have been asked to report their mean annual income.The data obtained are as follows.

Annual income in dollarsTexas33478,34817,32408,36597,34546,30887,34434,30260,33412,32163

Virginia34561,45128,37854,35506,42286,30611,33637,28510,34096,42427

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Thepopulation standard deviationfor mean annual income of teachers in Texas and in Virginia are estimated as6100

and6300

, respectively. It is also known that both populations are approximatelynormally distributed. At the0.01

level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of Texas is greater than or equal to the mean annual income of teachers in Virginia? Perform aone-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult alist of formulas.)

Thenull hypothesis:H

0

:

Thealternative hypothesis:H

1

:

The type oftest statistic:(Choose one)

Z

t

Chi square

F

The value of the test statistic:

(Round to at least three decimal places.)

Thep-value:

(Round to at least three decimal places.)

Can we reject the claim that the mean annual income of teachers from Texas is greater than or equal to the mean annual income of teachers from Virginia?

Yes

No